tlie object. From the two figures a c', b' c', for example,
the third figure a' b' may be compounded, by merely draw-
ing the vertical lines c h, b' i, and o' k, c l, to meet the
plane d e, and by producing them horizontally till they
meet and form the figure a b'. Similarly, the figure b' C
may be deduced from the other two by the aid of the lines
h, i, from a b', and the lines m, n, from a' c.

It is exactly in this way that a third view of any piece
of machinery is to be found from two given views ; and
it is evident that, in many cases, two elevations, or one
elevation and a plan, may be sufficient to afford a distinct
and complete idea of the construction of a machine. It is
obvious, at the same time, that, in other cases, many parts
may be concealed by others in which they are inclosed,
and by parts in the foreground, with reference to a parti-
cular projection. This suggests the occasional necessity,
not only of three projections, but also of imaginary views
of the interior of a machine, in which the machine is
supposed to be cut across, like an orange, by planes,
vertically or horizontally, so as properly to reveal its
structure. Such views are termed sections, and, with
reference to the planes of section, are denominated verti-
cal and horizontal sections. To all such drawings are
given the general title of geometrical drawings, as dis-
tinguished from perspective drawings.

Learners will be greatly assisted in forming their con-
ceptions of the meaning of geometrical drawings, by
minutely comparing detailed examples with the ma-
chines which they are meant to represent.

SECTION II.

Of Scales.

The first thing to be done, towards the execution of a
drawing upon paper, is to determine the scale upon which
the drawing is to be made. By the scale is meant the
proportion which the actual dimensions of the drawing
bear to those of the machine which it represents. Draw-
ings are made on various scales, according to circum-
stances, depending upon convenience for portability and
reference, and also upon the minuteness or largeness of
individual parts of the machine. The mechanism of a
watch, for example, is actually so minute, compared with
ordinary machinery, as, for example, a steam-engine of
20 horse power, that while no one would hesitate to make
a drawing of the former on a scale of equal magnitude for
practical purposes; the latter, to be brought within the
compass of an ordinary sheet of paper, would require to
be drawn upon a scale of reduced magnitude, to the
extent, say, of one-twelfth its lineal dimensions. An
ordinary turning-lathe might be drawn one-sixth full
size; and a suspension-bridge would be reduced two or
three hundred times its real size.

These remarks point to the necessity of suiting to cir-
cumstances the scales to which a machine is to be drawn.
But, again, it frequently occurs that the same machine
contains parts of considerable magnitude of outline, and
others of comparative minuteness ; so that a scale which
might suit the larger parts, would involve the smaller in
confusion, or would at least render the drawing unavail-
able for conveying more than a general idea of their form.
This circumstance, when it happens, renders necessary
detail dravjings, or separate drawings of those individual
minute parts upon a larger scale than the whole machine
is done to ; or even full-size drawings, when the parts are
of importance, and not too large.

The sccde of a drawing has reference to the proportion
of its lineal magnitude to that of the machine; it has
nothing to do with superficial magnitude, or area. It is
of some use to bear in mind this distinction, for superfi-
cial magnitude increases or diminishes much more rapidly
than lineal magnitude. In a drawing done to a scale of
one-half full size, for example, the lineal dimensions are
drawn one-half their actual magnitude, while the super-
ficial area of each part is reduced to one-fourth. A scale
is frequently designated by the inches or portion of an
inch of actual length, with which its parts are drawn to
represent one-foot length of the machine. Thus, a one-
half scale is termed also a six-inch scale, as six inches are
one-half of a foot; a scale of one-sixth is also called a two-
inch scale ; and a scale of one-twenty-fourth a half-inch
scale, as one foot contains half an inch twenty-four times.

HoltzapfelTs “ Ordinary Drawing Scales,” on card-board,
are very serviceable, as by their use dimensions can be set
off on the sheet, by the pricker or pencil, without the aid
of the dividers. When separate scales are not employed,
the scale of the proposed drawing should be laid down for